Method of analyzing moving objects using a vanishing point algorithm

ABSTRACT

A process of video capture, segmentation, tracking, and mapping to obtain position and time data for motion analysis. The moving object is captured in video in a series of frames at a known frame rate. The moving object is isolated from all other data in a frame and the position of the moving object is determined relative to stationary reference elements in the frame. However, the video captures a physical, three-dimensional space, in a two-dimensional image, causing distortions. This method associates all points in the quadrilateral with a rectangle defined by sides in real, physical space using a vanishing point algorithm. The preferred vanishing point algorithm maps a physical space to a quadrilateral defined by two sides that intersect at a first vanishing point, and two other sides that intersect at a second vanishing point. Single-point or three-point perspective may also be employed. Once associated, the position in the quadrilateral can be translated to Cartesian coordinates in the rectangle, thereby permitting the accurate determination of an object&#39;s position in physical space from a two-dimensional image. The algorithm correlates the midpoint on a side of the quadrilateral from the frame to the midpoint on a side of the rectangle in physical space.

FIELD OF INVENTION

This invention relates generally to tracking moving objects captured invideo and performing motion analysis on these objects.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of co-pending U.S. ProvisionalApplication No. 60/632180 filed Nov. 30, 2004, which is incorporated byreference herein.

BACKGROUND

Video recordings of live events are now commonplace: sporting events,gamblers in casinos at the various gaming tables, shoppers in stores,passengers moving through airports and bus terminals, etc. Mostfrequently the recorded data is analyzed only visually by the viewer,either as the event is taking place, or later, for example after a thefthas taken place from a store. Sporting events are recorded and playedback by coaches and players for analysis of athletic form. For example,football training camps are recorded on video and played back toevaluate individuals' skills and play execution. It would be useful tobe able to analyze the data systematically by methods other than simplyviewing the video.

Sometimes individual frames of the video are printed, providing an imageof one moment in time over a period of motion. The prior and post actioncannot be seen in the single image. It would be desirable tosimultaneously show multiple moments in time on a single image.

It is also desirable to determine the velocity or acceleration of anobject. For example, in an effort to determine how quickly an athletemoves from one position to another, a coach uses a stopwatch to time theathlete from start to finish. However, stopwatch measurements can beinaccurate. It would be desirable to accurately determine velocity andacceleration from a video recording, especially in the event the athletecannot be easily timed while performing, for example in a gamesituation.

SUMMARY OF THE INVENTION

The present system provides a method of analyzing the motion of one ormore objects. The preferred embodiment of the present system uses aprocess of video capture, segmentation, tracking, and mapping to obtainposition and time data. The data are analyzed to determine the desiredmotion information about the object, such as velocity and acceleration.

The moving object is captured in video in a series of frames at a knownframe rate. The moving object is isolated from all other data in a frameand the position of the moving object is determined relative tostationary reference elements in the frame. The position of the movingobject in the video is translated to a position in physical spaceutilizing a vanishing-point algorithm. The process is repeated formultiple frames. The distance the object has moved from one frame to thenext is calculated from the difference between the position in the firstframe and the position in the second frame.

The video captures a physical, three-dimensional space, in atwo-dimensional image, causing distortions. For example, parallel linesin physical space appear to converge in a video frame. So, a rectanglein a physical space looks like a quadrilateral in a video frame. Itfollows, then, that all points in a quadrilateral can be associated witha rectangle defined by sides in real, physical space.

The preferred vanishing point algorithm maps a physical space to aquadrilateral defined by two sides that intersect at a first vanishingpoint, and two other sides that intersect at a second vanishing point.Once associated, the position in the quadrilateral can be translated toCartesian coordinates in the rectangle, thereby permitting the accuratedetermination of an object's position in physical space from atwo-dimensional image. The algorithm may instead use one-pointperspective in which the quadrilateral will have only two edges parallelto each other, in which the second vanishing point can be considered tobe at an infinitely far away location. The vanishing point algorithmtakes advantage of the fact that the midpoint on a side of aquadrilateral can always be associated with a midpoint on the rectangle,such that the midpoint of a side of the quadrilateral from the frame iscorrelated with a point on a rectangle in physical space.

The method allows any desired information about the object's movement tobe obtained, provided the desired information can be determined fromposition and time. The method has particular applicability to sports,casino monitoring, traffic control, security and kinetic studies.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a single frame from a video of a football game showing how aquadrangle in the frame translates to a rectangle in physical space

FIG. 2 a is an original image before a simple binary dilation operation.

FIG. 2 b is an image after simple binary dilation operation on theoriginal by one pixel.

FIG. 3 illustrates 8-neighborhood connected components labeling.

FIG. 4 a is a schematic illustration of a single frame at a first time.

FIG. 4 b is a schematic illustration of the single frame at a secondtime.

FIG. 5 illustrates a quadrilateral using two vanishing points.

FIG. 6 illustrates the quadrilateral's diagonals and center point usingtwo vanishing points.

FIG. 7 illustrates the two-point quadrilateral's midpoints using twovanishing points.

FIG. 8 illustrates a quadrilateral using a single vanishing point.

FIG. 9 illustrates the quadrilateral's diagonals and center point usinga single vanishing point.

FIG. 10 illustrates the steps of shifting the quadrilateral to containthe point of interest within the quadrilateral.

FIG. 11 illustrates the steps of subdividing the quadrilateral tocontain the point of interest in a smaller quadrilateral.

FIG. 12 illustrates ghosting.

FIG. 13 illustrates stop framing.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is used to extract, position, time, and directiondata from a video recording of a real event occurring in real,three-dimensional space, referred to herein as physical space. Thepresent invention accomplishes this using a process of video capture,segmentation, tracking, mapping, data consolidation and analysis.

A video is recorded of a desired moving object moving in physical spaceby methods known in the art. FIG. 1 shows a single frame from a video ofa football game. As used herein, video means the stored electronicsignals that represent moving images over time. The signals may beanalog or digital, in a compressed or uncompressed format. Preferablythe video comprises a series of frames taken over time, where each framerepresents a set of data for a given moment in time such that frames puttogether, one after another, simulate motion. A video can be transmittedat a rate specified by number of frames per second or the amount of timebetween switching frames, both referred to herein as the frame rate.Video is commonly transmitted to a monitor or television to be displayedfor human viewing, but the invention herein can operate solely on thestored electronic signals. Visual display is preferred but notnecessary.

Once the movement is captured in video, the object of interest isisolated from other objects in the video. This process is referred toherein as segmentation. In general, a region of interest is selectedthat is constant across the series of frames. The moving object islocated within the region of interest and the region of interest can bein any shape but is preferably a quadrilateral. Data outside the regionof interest are not processed, leaving only the region of interest tohelp reduce processing time. Data regarding stationary objects in theregion of interest are also removed using a process known in the art asbackground subtraction. In addition to non-processed data outside theregion of interest, static data within the region of interest aresubtracted out. Individual frames of the video are compared and the datathat does not change is removed. The data remaining after the backgroundhas been subtracted out describes the moving object.

Methods of background subtraction are known in the art. One of thesimplest background subtraction techniques is to calculate an averageimage of the scene with no moving objects, subtract each new frame fromthis image, and threshold the result. More complex methods inlcude thatdiscussed in the paper by G. R. Bradski and J. W. Davis entitled “Motionsegmentation and pose recognition with motion history gradients.” Thepreferred embodiment uses binary silhouette-based image approach basedon color and luminosity differences, as explained in more detail below.In general, a binary silhouette image is generated for a single frame. Afilter is applied to the region of interest to mask out the background.Connected components labeling is applied for object detection and anobject merging procedure is repeated until there is no change in thenumber of different objects. Object tracking is applied to the isolatedobject.

Three color channels of the reference image are used for backgroundsubtraction. A binary different image is generated based on the maximumdifference of the three color channels between the current frame and thereference image. If the difference of a pixel is above the giventhreshold, the pixel value of the binary different image is set towhite, or “1”; otherwise the pixel is set to black, or “0”. Then abinary morphology operation is applied to the different image to connectany small regions, which may have become disjoint. The simple binarydilation can be implemented by simply changing any black pixel intowhite pixel, if it has at least one white neighbor. FIG. 2 a shows animage before a simple binary dilation operation, and FIG. 2 b shows thesame image after the operation is performed. Thus the binary silhouetteimage is generated.

Subsequently, a simple masking operation is applied to the binarysilhouette image to mask out all except the region of interest. Anypixel that is outside the region of interest will be set to zero. Next,a traditional connected components labeling module is applied to thebinary image after the region-of-interest masking. Connected componentlabeling works by scanning an image, pixel by pixel (from top to bottomand left to right) in order to identify connected pixel regions (i.e.,regions of adjacent pixels which have the same set of intensity values).The connected components labeling operator scans the image by movingalong a row until it comes to a point p (where p denotes the pixel to belabeled at any stage in the scanning process) for which p is white. Whenthis is true, it examines the four neighbors of p that have already beenencountered in the scan (i.e., the neighbors (i) to the left of p, (ii)above it, and (iii and iv) the two upper diagonal terms). Based on thisinformation, the labeling of p occurs as follows:

-   -   if all four neighbors are 0 (black), assign a new label to p,        else    -   if only one neighbor is 1 (white), assign its label to p, else    -   if one or more of the neighbors are 1 (white), assign one of the        labels to p and make a note of the equivalences.

See FIG. 3. After completing the scan, the equivalent label pairs aresorted into equivalence classes and a unique label is assigned to eachclass. As a final step, a second scan is made through the image, duringwhich each label is replaced by the label assigned to its equivalenceclasses. The connected components labeling can be implementedrecursively. The algorithm is summarized as follows:

-   -   Scan the image from left to right, top to bottom;    -   Find an “unlabeled” pixel with value “1” and assign a new label        to it;    -   Assign recursively all its neighbors with value “1” the same        label;    -   If there are no more unlabeled pixel with value “1” then stop.

Each connected component is considered an object in the frame. The masscenter of each object is calculated based on the weighted average of thelocation of each object pixel. A low-limit for number of object pixelsis used to filter out small objects. If the distance between twoobjects' center is less than certain threshold, then these two objectswill be merged as one object. The process will be repeated until thenumber of objects is unchanged.

The moving object's motion is correlated from frame to frame. Forregions of interest having only one moving object, this isstraightforward. However, if other moving objects that are not ofinterest are introduced to the region of interest, their motion must bekept separate from that of the object of interest. For example, assumethe object of interest is a football player on a playing field and theregion of interest in the video shows the sky in the background. If ajet flies by in the sky, it is a moving object that will be segmentedout and yet is uninteresting. So, the motion from the jet must be keptseparate from that of the player. This is accomplished by correlatingthe motion of the player from frame to frame so that it is notco-mingled with the motion of the jet. To track the moving object andeliminate unwanted objects, objects are grouped with those in closeproximity having similar motion.

Once the moving object is isolated, its position is determined using avanishing point algorithm. As is known in art and geometry, recedingparallel lines will appear to converge at a point on the horizon, knownas the vanishing point. This fact of nature allows two-dimensionalimages such as paintings and video to convey three-dimensional distance.For example, to create and illusion in a painting that a train is comingout of the painting towards the viewer, the engine of the train would besignificantly larger than the caboose, although in physical space theengine and caboose are approximately the same size.

The video captures a physical, three-dimensional space, in atwo-dimensional image, causing distortions. For example, parallel linesin physical space appear to converge in a video frame. So, a rectanglein a physical space looks like a quadrilateral in a video frame. Itfollows, then, that all points in a quadrilateral can be associated witha rectangle defined by sides in real, physical space.

To determine the position of an object in physical space from a videoframe, the object's position must be correlated from the video to thephysical space, taking into account the effect of the perspectiveprojection. Due to the nature of the vanishing points, a given distancein the physical space correlates to different distance in mathematicalcoordinates, depending on the position of the object with respect to thevanishing point. This would seem to make it more difficult to determinethe distance in the video that an object travels, because a measurementin the video does not give an accurate distance in physical space.

However, the location of any point lying on a plane in a two-dimensionalimage, such as a video frame, can be identified in physical space bymapping a quadrilateral on the frame to a rectangle on the plane in thephysical space. See FIGS. 1, 4 a and 4 b. The position of the object inthe frame is defined by coordinates referred to herein as “mathematicalcoordinates” and the object in physical space is defined by coordinatesreferred to as “physical coordinates”. Thus, the vanishing pointalgorithm maps a quadrilateral to a square.

The dimensions of the quadrilateral in the frame are determined byselecting stationary reference elements in the physical space to definethe boundaries of the quadrilateral. Stationary references are chosensuch that the distance between them can be accurately determined inphysical space, preferably by selecting elements with known spacing orby taking physical measurements at the space. The relationship betweenthe position in the frame and the position in physical space can becalculated using trigonometry, using right triangle measurements andratios. The computational power and time required for such calculationsis significant, however. Instead, the preferred embodiment uses asimpler method relating the midpoints of corresponding lines in thequadrilateral and in the physical space, as explained in more detailbelow.

To facilitate understanding of the invention, a football field is usedas the desired physical space. See FIG. 1. The 45 yard line, indicatedas A-B, determines the first side of the quadrilateral. The 35 yardline, indicated as C-D, determines the second side of the quadrilateral.The sideline, indicated as A-D, determines the third side of thequadrilateral, and the hash marks, indicated as B-C, indicate the fourthside of the quadrilateral. None of the sides in this quadrilateral areequal in length or orientation, and none of the angles between the sidesare 90°.

Once the coordinates of the quadrilateral in the two-dimensional planeare determined, they can be mapped to analogous points in the physicalplane, for example the football field. The quadrilateral's similarlyoriented edges are extended until they intersect. These intersectionsare the vanishing points u and v. See FIG. 5. The present invention canalso be applied in one-point perspective system, where two sides of thequadrilateral are parallel to each other and only one vanishing pointwill be used. See FIGS. 8 and 9. In the one-point quadrilateral, two ofthe quadrilateral's similarly oriented edges are extended until theyintersect at vanishing point s. The second vanishing point can beconsidered at an infinitely far away location. Instead of using thesecond vanishing (v) and the center point (O) to form the second axis,the second axis will be formed by the line passes through the centerpoint (O). but parallel to the two edges. All the remaining x and ymeasurements will be the same as in the two-point case. Similarly, thepresent invention can be applied using three vanishing points. Themathematical coordinates are mapped to the physical coordinates byassociating points A to A′, B to B′, C to C′ and D to D′.

For example, FIG. 1 shows a football field. The yard lines arestationary reference elements that can be measured in physical space.The distance between each yard line in physical space is 5 yards, so thedistance between line A′ B′ and line C′ D′ is 30 feet. The midpoint ofline AD on the quadrilateral is equivalent to the midpoint on the lineA′ D′ of the rectangle, so the distance from A to the midpoint of lineAD is 15 feet. The sideline and hash marks are also stationary referenceelements can be measured in physical space; the distance between theline A′ D′ and line B′ C′ in physical space is 89 feet 3 inches. Again,the midpoint of line AB on the quadrilateral is equivalent to themidpoint on the line A′ B′ of the rectangle, so the distance from A tothe midpoint of line AB is 44.625 feet. The quadrilateral can be shiftedand subdivided such that the object of interest is located essentiallyon a midpoint, as described in more detail below, thereby easilydetermining the object's position in physical space.

Note that the present invention can be applied to any three-dimensionalspace having stationary features that serve as reference geometries.These spaces include but are not limited to, sports fields (includingthose other than football), casinos, gaming tables, shopping counters,malls, and city streets.

To further facilitate understanding of the invention, a casino table isused in a second example as the desired physical space. See FIG. 4. Aportion of the playing surface where the chips are exchanged has beenisolated from video supplied by security cameras, and is referred to asthe table. The first side of the table, indicated as A-B, determines thefirst side of the quadrilateral. The second side of the table, indicatedas C-D, determines the second side of the quadrilateral. The third sideof the table, indicated as A-D, determines the third side of thequadrilateral, and the fourth side of the table, indicated as B-C,indicates the fourth side of the quadrilateral. None of the sides arenecessarily equal in length or orientation.

The quadrilateral defined by ABCD is translated to a square A′ B′ C′ D′.The position of a chip 17 on the table in a first frame is illustratedin FIG. 4 a. The physical coordinates of the chip at a first time (t₁)are (x,y)₁. FIG. 4 b shows that the chip has moved. The physicalcoordinates of the chip at a second time (t₂) are (x,y)₂. The differencebetween position (x,y)₁ and position (x,y)₂ is the distance the chiptraveled in the time between t₁ and t₂.

For accuracy, precision, and speed, it is desirable to choose aquadrilateral that is easily defined by reference elements. However,sometimes the object of interest may not be in the most-easily definedquadrilateral. If the object of interest is not inside the givenquadrilateral, the quadrilateral must be shifted along the horizontal orvertical axes, or both, until it surrounds the object of interest. Thequadrilateral can be shifted in any direction, but for purposes ofillustration, the figures show a quadrilateral being shifted to theleft. FIGS. 5-7 and 10-11 show the process using the system with twovanishing points. The process to shift the quadrilateral to contain theobject of interest is:

-   -   Determine the center point O of the quadrilateral. The center        point O is the intersection point of the quadrilateral's        diagonals. See FIG. 6.    -   Determine the midpoint of each edge. Each edge's midpoint is the        intersection of that edge with the line that passes through the        vanishing point u and O or v and O. These midpoints will help        form the shifted quadrilateral. See FIG. 7.    -   In this step, the quadrilateral begins its shift toward the        point of interest. The edge of the quadrilateral nearest the        point of interest will be referred to as the edge E. Find the        line L₁ that passes through the midpoint of edge E and the        midpoint of one of its adjacent edge. Find the intersection        point of L₁ and the adjacent edge. This will be the third point        to help form the shifted quadrilateral.    -   Repeat the previous step, but swap the adjacent edges to find        the line L₂ that passes through the midpoint of edge E and the        midpoint of one of other adjacent edge. Find the intersection        point of L₂ and the adjacent edge. This will be the fourth point        to help form the shifted quadrilateral.    -   Adjust the mappings to reflect the shift.

Repeat the steps until the point of interest is inside thequadrilateral.

If the quadrilateral is small enough, it will accurately indicate theposition of the object of interest. However, for increased accuracy, thequadrilateral can be subdivided. The smaller the quadrilateral, the moreaccurate the position of the object within it is determined. Theaccuracy of the method depends on the level of subdivision that occurs.For more accurate mappings, the subdivision can be repeated until thearea of the resulting quadrilaterals nears zero.

The process to subdivide the quadrilateral to contain the object ofinterest is:

-   -   Determine the center point O of the quadrilateral. The center        point O is the intersection point of the quadrilateral's        diagonals See FIG. 6.    -   Determine the midpoint of each edge. Each edge's midpoint is the        intersection of that edge with the line that passes through the        vanishing point u and O or v and O.    -   Form four smaller quadrilaterals out of the corner points, the        center point and midpoints (see FIG. 11). Create the mappings        for the new quadrilaterals.    -   Determine which of the new quadrilaterals the point of interest        lies in. If more accuracy is desired, subdivide the        quadrilateral again.

Each processed frame has a significant amount of information associatedwith it, including the location of each centroid, the object's masscenter, the quadrilateral, multiple objects in the region of interest,etc. In the preferred embodiment the data is consolidated and data isorganized into files. Files may be referenced by some index file orconcatenated into a single archival file. Organizing and consolidatingthe information helps facilitate quicker processing with fewer errors.

Positional data is used in combination with frame rate to derivevelocity, acceleration and distance. For example, to determine the speedof a football player leaving the line of scrimmage, the grid coordinatesof the player's start and finish positions are entered into thecomputer. Data entry can be input by any known method. The preferredmethod of data input is clicking a mouse when the cursor overlies thedesired position on the monitor. The player's start grid coordinates aresubtracted from his finish grid coordinates to determine the distancetraveled. The amount of time it took is determined by the number offrames elapsed divided by the video frame rate. The player's speed isdetermined by dividing the distance by the time. Consequently, thedesired metrics are output and used to compare and improve a player'smotion.

The metrics are accurate to within Nyquist sampling of the frame rate.So, if a coach using a stopwatch makes an error on starting or stoppingthe stopwatch of more than 1/30^(th) of a second, the present process ismore accurate.

For manual analysis, the video data is supplied to a receiver and theimage with the quadrilateral is displayed on a monitor. The row andcolumn coordinates on the monitor relate to specific positions on thefootball field. For convenience, the two-dimension grid coordinates arethe row and column coordinates of the pixels of the monitor. In otherwords, each set of pixel coordinates on the monitor translates to aspecific position on the football field. For example in FIG. 1, usingthe origin (0,0) as indicated, player a is at pixel grid position (360,240) on the monitor, translating to the 42.12 yard line and 26.49 yardsfrom the origin, respectively.

However, the preferred embodiment is automated. The video data issupplied to a receiver and the quadrilateral reference image iscalculated digitally and recorded. The two-dimension grid coordinatesare simply x,y arithmetic coordinates. No visual monitor is needed. Theresultant coordinate table that consolidates desired three-dimensionalspace to the two-dimensional map coordinates is a tangible result usedfor determination of position.

Another result of the present device is the ability to extract themotion data and simultaneously show multiple positions in time on asingle image. FIG. 12 shows a schematic illustration of ghosting, whichis used to visually depict the object's motion and acceleration. Thesingle image captured from a still position of the moving object isstacked next to the captured still position of the moving objectdetected next in time. The stills collected on the single output therebysimultaneously show multiple positions over time. The closer the imagesare stacked together indicates a slower period of acceleration.

FIG. 13 shows a schematic illustration of stop framing, which is used tovisually depict the distance traveled in a given period of time. Thesingle image captured from a still position of the moving object isstacked next to another captured still position of the moving objectdetected later in time. The single image then simultaneously showsmultiple positions over a period of time. The closer the images arestacked together indicates a smaller distance traveled for a givenperiod of time.

While there has been illustrated and described what is at presentconsidered to be a preferred embodiment of the present invention, itwill be understood by those skilled in the art that various changes andmodifications may be made, and equivalents may be substituted forelements thereof without departing from the true scope of the invention.Therefore, it is intended that this invention not be limited to theparticular embodiment disclosed as the best mode contemplated forcarrying out the invention, but that the invention will include allembodiments falling within the scope of the appended claims.

1. A method of performing motion analysis on an object moving inphysical space, the method comprising determining the position of theobject by: a) recording movement of the object in video; b) isolatingthe object from background data in a frame of the video; c) containingthe object in a quadrilateral in the frame; d) determining a rectanglein physical space corresponding to the quadrilateral; e) associating thequadrilateral with the rectangle such that a first point in thequadrilateral defines a physical location defined by a correspondingfirst point in the rectangle; and f) recording the physical location ofthe object.
 2. The method of claim 1 wherein the quadrilateral has foursides and two of the sides define a first vanishing point in the frame.3. The method of claim 1 wherein the quadrilateral has four sides andtwo of the sides define a first vanishing point in the frame and theother two sides define a second vanishing point in the frame.
 4. Themethod of claim 2 wherein the first point in quadrilateral is themidpoint of a side of the quadrilateral and the corresponding firstpoint in the rectangle is the midpoint of a corresponding side of therectangle.
 5. The method of claim 1 wherein isolating the object frombackground data in a frame of the video is accomplished with binarysilhouette background subtraction.
 6. The method of claim 1 wherein thephysical space is an athletic field.
 7. A method of performing motionanalysis on a moving object comprising: a) recording movement of theobject in video at a frame rate, the video comprising at least a firstframe and second frame; b) isolating the object from background data inat least the first frame and the second frame; c) in the first frame,containing the object in a quadrilateral having mathematical coordinatesA, B, C and D, where: i. the side defined by A-B and the side defined byC-D, if extended, would intersect at a first vanishing point u; and ii.the side defined by A-D and the side defined by C-B, if extended, wouldintersect at a second vanishing point v; d) determining a rectangle inphysical space having physical coordinates A′, B′, C′ and D′, where: i.the side defined by A′-B′ and the side defined by C′-D′ are parallel;ii. the side defined by A′-D′ and the side defined by C′-B′ areparallel; e) associating the quadrilateral with the rectangle such thata first point on a side in the quadrilateral defines a physical locationdefined by a corresponding point on a corresponding side in therectangle; f) determining the physical location of the object containedby the quadrilateral by associating the mathematical coordinates of thequadrilateral to the physical coordinates of the rectangle; g) repeatingsteps c-f for the object in the second frame; and h) recording thedistance the object traveled as the difference between the physicallocation of the object in the first frame and the physical location ofthe object in the second frame.
 8. The method of claim 7 wherein thefirst point on the side in the quadrilateral is the midpoint of thatside and the corresponding point on the corresponding side in therectangle is the midpoint of that side of the rectangle.
 9. The methodof claim 7 further comprising: a) determining the time elapsed betweenthe first frame and the second frame from the frame rate; b) dividingthe distance the object traveled by the time elapsed; and c) recordingthe result as the velocity of the object.
 10. The method of claim 7wherein containing the object further comprises subdividing thequadrilateral to achieve a desired accuracy.
 11. The method of claim 7wherein containing the object further comprises shifting thequadrilateral to achieve a desired accuracy.
 12. A method of determiningthe acceleration of an object comprising: a) determining a firstvelocity of an object from the method of claim 9; b) using a secondframe and a third frame, determining a second velocity of the objectfrom the method of claim 9; c) obtaining the difference between thefirst velocity from the second velocity and dividing that distance bythe time elapsed; and d) recording the result as the acceleration of theobject.
 13. The method of claim 7 wherein the physical space is anathletic field.
 14. A method of performing motion analysis on a movingobject comprising: a) capturing movement of the object in video at aframe rate, the video comprising at least a first frame and secondframe; b) segmenting the object from background data in at least thefirst frame and the second frame; c) tracking the object from theposition in the first frame to the position in the second frame; d)mapping the object by correlating the object's position in each frame tothe object's position in physical space by relating the object'sposition along a vanishing point line in the each frame to a positionalong a reference line in physical space; and e) recording the result ofstep d.
 15. The method of claim 14 wherein the position along avanishing point line in the first frame is the midpoint of thatvanishing point line and the correlated position is a midpoint along areference line in physical space.
 16. The method of claim 14 whereinsegmentation comprises binary silhouette background subtraction.
 17. Themethod of claim 14 wherein the physical space is an athletic field. 18.The method of claim 14 wherein the physical space is one of a casino, astore, an airport, or a bus terminal.
 19. The method of claim 14 furthercomprising displaying the object in more than one position in physicalspace in a single image.
 20. The method of claim 14 further comprisingstacking a display of the object in position next to another position ofthe object detected next in time.